The Study of Astronomy, adapted to the capacities of youth / In twelve familiar dialogues, between a tutor and his pupil: explaining the general phænomena of the heavenly bodies, the theory of the tides, &c.

by teacher of astronomy John Stedman

Tutor. What I have now explained relates not only to the primary planets which have the sun for their center of motion; but, you must remember that the secondary planets are governed by the same laws, in revolving about their respective primaries; for, as by the attractive power of the sun combined with the projectile force of the primary planets they are retained in their orbits; so also the action of the primaries upon their respective secondaries together with their projectile force, will preserve them in their orbits.

Pupil. Pray, Sir, what have you else to observe?

Tutor. Have I not told you that the orbits of the planets are not true circles, but a little elliptical?

Pupil. Yes, Sir; and I shall be glad to know the reason of it.

Tutor. If the attractive power of the sun were uniformly the same in every part of their orbits they would be true circles, and the planets would pass over equal portions of their orbits in equal times; that is, they would move from B to C, (Plate II. fig. 5.) in the same time as from A to B, &c.

Pupil. That is clear, but as their orbits are elliptical, when the planets are farthest from the sun, the velocity with which they move must be lessened as the attraction is decreased.

Tutor. And they must consequently pass over unequal parts of their orbits in equal portions of time. And, as a double velocity will balance a quadruple or fourfold power of gravity or attraction, it follows, that as the centripetal force is four times as great at A as at B (Plate II. fig. 4.) the centrifugal force will be twice as great, and would carry a planet from A to a in the same time it would from B to b, and in its orbit from A to c as soon as from B to d, and thereby describe the area, or space contained between the letters A S c, in the same time as the area or space B S d. For according to the laws of the planetary motions, in their periodical revolutions, they always describe equal areas in equal times.

Pupil. The orbits of the comets being very elliptical, the irregularity of their motions must be exceedingly great.

Tutor. Great, indeed!—One of them passed so near the sun as to acquire a heat which Sir Isaac Newton computed to be two thousand times hotter than red hot iron.[^[12]]

Pupil. Astonishing! If they pass so near the sun, the centripetal force must act powerfully on the body of the comet.